Title:The coronal X-ray - age relation and its implications for the evaporation of exoplanets

Abstract: We study the relationship between coronal X-ray emission and stellar age for
late-type stars, and the variation of this relationship with spectral type. We
select 717 stars from 13 open clusters and find that the ratio of X-ray to
bolometric luminosity during the saturated phase of coronal emission decreases
from 10^-3.1 for late K-dwarfs to 10^-4.3 for early F-type stars (across the
range 0.29<(B-V)_0<1.41). Our determined saturation timescales vary between
10^7.6 and 10^8.3 years, though with no clear trend across the whole FGK range.
We apply our X-ray emission - age relations to the investigation of the
evaporation history of 121 known transiting exoplanets using a simple
energy-limited model of evaporation and taking into consideration Roche lobe
effects and different heating/evaporation efficiencies. We confirm that a
linear cut-off of the planet distribution in the M^2/R^3 versus a^-2 plane is
an expected result of population modification by evaporation and that the known
transiting exoplanets display such a cut-off. We find that for an evaporation
efficiency of 25% we expect around 1 in 10 of the known transiting exoplanets
to have lost > 5% of their mass since formation. In addition we provide
estimates of the minimum formation mass for which a planet could be expected to
survive for 4 Gyrs for a range of stellar and planetary parameters.
We emphasise the importance of the earliest periods of a planet's life for
its evaporation history with 75% expected to occur within the first Gyr. This
raises the possibility of using evaporation histories to distinguish between
different migration scenarios. For planets with available spin-orbit angles no
difference is found between the distributions of planets with misaligned orbits
and those with aligned orbits. This suggests that misalignment occurs early in
the life of the planetary system, though more data is needed.

Comments:

20 pages, 14 figures, accepted by MNRAS. Full versions of Tables 3, 4 and 5 available with the online journal version